{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:4OJIXHEKO3ACEZUTBL25XB3USH","short_pith_number":"pith:4OJIXHEK","canonical_record":{"source":{"id":"1309.7914","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-30T16:45:41Z","cross_cats_sorted":[],"title_canon_sha256":"841cda0bb39a4699af8bfddaaecc381b5d1d8bfe760ea2aa2331b788e8b78bd1","abstract_canon_sha256":"ae87716d1afda44b17d496aaba9d931cb26548de839d39f6215df76c4fa059c0"},"schema_version":"1.0"},"canonical_sha256":"e3928b9c8a76c02266930af5db877491ff68c3a820313368c08c685a3bf34dd4","source":{"kind":"arxiv","id":"1309.7914","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7914","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7914v1","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7914","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"pith_short_12","alias_value":"4OJIXHEKO3AC","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4OJIXHEKO3ACEZUT","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4OJIXHEK","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:4OJIXHEKO3ACEZUTBL25XB3USH","target":"record","payload":{"canonical_record":{"source":{"id":"1309.7914","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-30T16:45:41Z","cross_cats_sorted":[],"title_canon_sha256":"841cda0bb39a4699af8bfddaaecc381b5d1d8bfe760ea2aa2331b788e8b78bd1","abstract_canon_sha256":"ae87716d1afda44b17d496aaba9d931cb26548de839d39f6215df76c4fa059c0"},"schema_version":"1.0"},"canonical_sha256":"e3928b9c8a76c02266930af5db877491ff68c3a820313368c08c685a3bf34dd4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:47.809825Z","signature_b64":"v8vWwITW4uBQmvEfKAVUS5noBY/2zkTUkkq10NiSX5I/TW0lpjqh8SUlXCYyQRskbqiZdmT02YHvFhdgEA5gDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3928b9c8a76c02266930af5db877491ff68c3a820313368c08c685a3bf34dd4","last_reissued_at":"2026-05-18T03:11:47.809102Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:47.809102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.7914","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:11:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nzz3pr1WgpiDwThN6g1B1vwi2zKnAJE+3tUlgqcHZ85Dm1XrMGuMh1OC1nBOFDribxjMkyiTe19RX5oH86aEBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T05:01:45.805905Z"},"content_sha256":"6692e952e9c7a5be9aa05d48e6661ac57914d80abbdcdd1f892e31111a1a6f38","schema_version":"1.0","event_id":"sha256:6692e952e9c7a5be9aa05d48e6661ac57914d80abbdcdd1f892e31111a1a6f38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:4OJIXHEKO3ACEZUTBL25XB3USH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Procrustes problems and Parseval quasi-dual frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"G.Corach, M.Ruiz, P. Massey","submitted_at":"2013-09-30T16:45:41Z","abstract_excerpt":"Parseval frames have particularly useful properties, and in some cases, they can be used to reconstruct signals which were analyzed by a non-Parseval frame. In this paper, we completely describe the degree to which such reconstruction is feasible. Indeed, notice that for fixed frames $\\cF$ and $\\cX$ with synthesis operators $F$ and $X$, the operator norm of $FX^*-I$ measures the (normalized) worst-case error in the reconstruction of vectors when analyzed with $\\cX$ and synthesized with $\\cF$. Hence, for any given frame $\\cF$, we compute explicitly the infimum of the operator norms of $FX^*-I$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7914","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:11:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TCKOA0kkZ+CUhKXqQN3ocPc5/8Bric5zCDE9VeFhc5Iyz0FEPU5DYgyl5Ju3ePs9HYuGngEmuhHVlrlzKmUTBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T05:01:45.806509Z"},"content_sha256":"7d4e202031073fc5caf6033ff1ffcf89a323e7ace374e79a3b14b921b634e9ef","schema_version":"1.0","event_id":"sha256:7d4e202031073fc5caf6033ff1ffcf89a323e7ace374e79a3b14b921b634e9ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4OJIXHEKO3ACEZUTBL25XB3USH/bundle.json","state_url":"https://pith.science/pith/4OJIXHEKO3ACEZUTBL25XB3USH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4OJIXHEKO3ACEZUTBL25XB3USH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-23T05:01:45Z","links":{"resolver":"https://pith.science/pith/4OJIXHEKO3ACEZUTBL25XB3USH","bundle":"https://pith.science/pith/4OJIXHEKO3ACEZUTBL25XB3USH/bundle.json","state":"https://pith.science/pith/4OJIXHEKO3ACEZUTBL25XB3USH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4OJIXHEKO3ACEZUTBL25XB3USH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4OJIXHEKO3ACEZUTBL25XB3USH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ae87716d1afda44b17d496aaba9d931cb26548de839d39f6215df76c4fa059c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-30T16:45:41Z","title_canon_sha256":"841cda0bb39a4699af8bfddaaecc381b5d1d8bfe760ea2aa2331b788e8b78bd1"},"schema_version":"1.0","source":{"id":"1309.7914","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7914","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7914v1","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7914","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"pith_short_12","alias_value":"4OJIXHEKO3AC","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4OJIXHEKO3ACEZUT","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4OJIXHEK","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:7d4e202031073fc5caf6033ff1ffcf89a323e7ace374e79a3b14b921b634e9ef","target":"graph","created_at":"2026-05-18T03:11:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Parseval frames have particularly useful properties, and in some cases, they can be used to reconstruct signals which were analyzed by a non-Parseval frame. In this paper, we completely describe the degree to which such reconstruction is feasible. Indeed, notice that for fixed frames $\\cF$ and $\\cX$ with synthesis operators $F$ and $X$, the operator norm of $FX^*-I$ measures the (normalized) worst-case error in the reconstruction of vectors when analyzed with $\\cX$ and synthesized with $\\cF$. Hence, for any given frame $\\cF$, we compute explicitly the infimum of the operator norms of $FX^*-I$,","authors_text":"G.Corach, M.Ruiz, P. Massey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-30T16:45:41Z","title":"Procrustes problems and Parseval quasi-dual frames"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7914","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6692e952e9c7a5be9aa05d48e6661ac57914d80abbdcdd1f892e31111a1a6f38","target":"record","created_at":"2026-05-18T03:11:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ae87716d1afda44b17d496aaba9d931cb26548de839d39f6215df76c4fa059c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-30T16:45:41Z","title_canon_sha256":"841cda0bb39a4699af8bfddaaecc381b5d1d8bfe760ea2aa2331b788e8b78bd1"},"schema_version":"1.0","source":{"id":"1309.7914","kind":"arxiv","version":1}},"canonical_sha256":"e3928b9c8a76c02266930af5db877491ff68c3a820313368c08c685a3bf34dd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3928b9c8a76c02266930af5db877491ff68c3a820313368c08c685a3bf34dd4","first_computed_at":"2026-05-18T03:11:47.809102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:47.809102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v8vWwITW4uBQmvEfKAVUS5noBY/2zkTUkkq10NiSX5I/TW0lpjqh8SUlXCYyQRskbqiZdmT02YHvFhdgEA5gDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:47.809825Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7914","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6692e952e9c7a5be9aa05d48e6661ac57914d80abbdcdd1f892e31111a1a6f38","sha256:7d4e202031073fc5caf6033ff1ffcf89a323e7ace374e79a3b14b921b634e9ef"],"state_sha256":"b36b47fe0988ae65f598c8956496eb298eec232de00718aea23ef99b1e02e30c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pt0GyK+sIG/pqbxEDgN2cYAX08dwacwPMdBj4PWGBqGm1oY1GYFwevBIQktnn9LZf25uklyz9CZt66O3C8/ECQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T05:01:45.809730Z","bundle_sha256":"d7773d07fd6bb7a803617ec4df54f75d2ceb30f3372bc178554251813cf460b5"}}